1. Field of the Invention
The present invention relates to a method and to an apparatus for calculating motional characteristics of an object moving relative to a measuring structure, particularly of a projectile moving in a weapon barrel.
2. Description of the Prior Art
In general terms, in such techniques, an electromagnetic wave is directed from a measuring structure onto the object to be measured and is superimposed with the wave reflected by the object, the chronological curve of the phase difference between the forward wave and the return wave represented by an electrical measured signal is assigned to individual amplitude values of the appertaining phase difference and, therefore, to the respective location of the object, and the respective motional characteristics are calculated by differentiation of this phase difference with respect to time. The corresponding apparatus comprises a generator for generating an electromagnetic wave, a coupling arrangement in communication therewith for infeed of the electromagnetic waves into the barrel of the web, a mixing stage for superimposing a portion of the infed wave with the wave reflected by the projectile, a transient recorder for recording the electrical measured signal that represents the chronological curve of the phase difference between the transmitted wave and the return wave, and an evaluation device for the measured signal.
Methods and apparatus of the type set forth above are excellently suited for non-contacting measurement of the curve of velocity and acceleration of intrinsically arbitrary, moving objects but have recently achieved significance mainly in conjunction with what is referred to as internal ballistics of firearms. In addition to the gas pressure, the translational projectile motion in the barrel of the weapon, i.e. path, velocity and acceleration of the projectile, that is produced by the pressure of the projectile on the bottom is of central significance in internal ballistics. Methods of the above type are presently implemented in the caliber range from about 5-600 mm with commercially-available microwave interferometers.
Therefore, for example, U.S. Pat. No. 2,691,761, U.S. Pat. No. 2,735,981, and U.S. Pat. No. 2,824,284, all of which are incorporated herein by this reference, respectively disclose a method or, respectively, an apparatus of the above type, whereby the distance between neighboring maximums or, respectively, minimums of the registered interferometer signal is respectively measured and utilized for further processing in all cases for evaluating the electrical measured signal that represents the chronological curve of the phase difference between the transmitted and return waves. Since, given the assumption that no disturbing influences occur due to combustion gases that could be pressed in front of the projectile due to leaks, the local frequency of the Doppler shift is directly proportional to the velocity of the projectile at the respective location. An allocation on the one hand of the appearance of these maximums or, respectively, minimums to discrete locations along the length of the barrel of the weapon can occur by way of the known propagation wave lengths of the electromagnetic wave employed and, on the other hand, a defined velocity can be respectively assigned to a location at these locations by forming the difference quotient of a quantity proportional to the measured, chronological intervals.
Only point-by-point results at discrete times are thereby directly obtained from the actual measurement, this meaning that there is actually no steady, differentiatable signal curve. Mean velocities can, in fact, be respectively assumed between the individual extreme values, but these then change discontinuously at the extreme values themselves. In most case, a direct averaging over the discrete velocity values obtained in this manner leads to errors which cannot be compensated since, although the velocity is linearly dependent on the path, it is hyperbolically dependent on the time (velocity v=path s/time t--an averaging over the time therefore occurs in the denominator of the fraction). Further, great errors of course derive due to the measuring of the spacings of the extreme values themselves, since it cannot be guaranteed in discrete-time systems that the actual extreme values are also sensed and, therefore, each quantization error has a direct influence and causes additional error in the result supplied by the measurement that can practically not be corrected.
What is available as a second, somewhat more elegant method for calculating the local frequency and, therefore, discrete velocity or, respectively, acceleration values at a defined time or, respectively, at a defined location in the barrel of the weapon is short-time Fourier transformation which, in fact, already takes all registered amplitude values of the interferometer signal into consideration and therefore averages over the quantization and phase errors that are unavoidable in the measurement itself, but has further disadvantages that are founded on the nature of the method itself. Similar to the uncertainty relation, one thereby encounters the problem, expressed in general terms, that the product of the measuring time and frequency bandwidth is a constant value; when one therefore wishes to calculate the Doppler frequency and, therefore, the projectile velocity with great accuracy, the measuring time must be selected long, but this is impossible because of the highly-transient events.